Ken's POTW

Weekly Schedules

A league has N teams.
Devise a season schedule to let each team play every other team
exactly once (explain the method for making this schedule.)
Games are played at the same time each week. There are as many
locations to play as needed.
What is the minimum number of weeks needed for the season?

In a similar league, N teams begin a single elimination
tournament. What is the minimum number of games needed to determine
a champion team? What is the minimum number of weeks for the
tournament?